We develop a method to accurately and efficiently determine the vibrational free energy as a function of temperature and volume for substitutional alloys from first principles. Taking Ti 1−x Al x N alloy as a model system, we calculate the isostructural phase diagram by finding the global minimum of the free energy corresponding to the true equilibrium state of the system. We demonstrate that the vibrational contribution including anharmonicity and temperature dependence of the mixing enthalpy have a decisive impact on the calculated phase diagram of a Ti 1−x Al x N alloy, lowering the maximum temperature for the miscibility gap from 6560 to 2860 K. Our local chemical composition measurements on thermally aged Ti 0.5 Al 0.5 N alloys agree with the calculated phase diagram. DOI: 10.1103/PhysRevLett.117.205502 When discussing the solubility of an alloy, the configurational entropy is always taken into account, but the effect of temperature associated with lattice vibrations is often neglected. It has been experimentally shown [1][2][3][4] that the vibrational and configurational entropies are comparable in the cases of fcc Ni 3 Al and Cu 3 Au and bcc Fe 3 Al and FeCr, and theoretical studies draw the same conclusion [5][6][7][8][9][10] that lattice vibrations cannot be ignored. High-quality phonon spectra can be computed in the framework of density-functional perturbation theory [11] and the small displacement method [12], but the introduction of substitutional disorder as in an alloy causes the cost of such calculations to escalate rapidly. In this Letter, we propose a method of computing the vibrational free energy of a configurationally disordered solid based on the temperature-dependent effective potential method (TDEP) [13,14], which has an efficiency comparable to the stateof-the-art methods that only apply to ordered solids. Moreover, the method has the advantage of taking into account anharmonicity of the lattice vibrations and, therefore, remains valid at temperatures for which the quasiharmonic approximation breaks down.We demonstrate the accuracy of our technique in a study of decomposition thermodynamics of Ti 1−x Al x N alloys [15,16], a system for which lattice vibrations underpin an unusual and technologically useful isostructural decomposition [17]. Metastable Ti 1−x Al x N coatings are ideal for use in the manufacturing of cutting tools due to their characteristic age hardening during use [18]. Metastable Ti 1−x Al x N with cubic B1 crystal structure undergoes spinodal decomposition to form nanoscale domains of B1 TiN-and AlN-rich phases, through which extra stress is required to propagate dislocations [16,19,20]. Remarkably, the calculated values of the maximum temperature for the miscibility gap vary between approximately 7900 and 9000 K [21], depending on the methodological details, and as low as 3790 K [22] within the Debye-Grüneisen approximation. These are well above the dissociation temperatures of TiN and AlN, however, but cutting tools may reach temperatures of up to 1300 K [23], at wh...
Comparison of segregations formed in unmodified and Sr-modified Al-Si alloys studied by atom probe tomography and transmission electron microscopy, 2014, Journal of Alloys and Compounds, (611) AbstractThe mechanical properties of Al-7 wt.% Si can be enhanced by structural modifications of its eutectic phase. Addition of low concentrations of certain elements, in this case 150 wt-ppm Sr, is enough to cause a transition from a coarse plate-like Si structure to a finer coralline one. To fully understand the operating mechanism of this modification, the composition of the eutectic Si phase in unmodified and Sr-modified alloys was analysed and compared by Atom Probe Tomography and (Scanning) Transmission Electron Microscopy. The unmodified alloy showed nanometre sized Al-segregations decorating defects, while the Sr-modified sample presented three types of Al-Sr segregations: (1) rod-like segregations that promote smoothening of the Al-Si boundaries in the eutectic phase, (2) particle-like segregations comparable to the ones seen in the unmodified alloy, and (3) planar segregations favouring the formation of twin boundaries. Al and Sr solubilities in Si after solidification were determined to be 430 ± 160 at-ppm and 40 ± 10 at-ppm, respectively. Sr predominantly segregates to the Si phase confirming its importance in the modification of the eutectic growth.
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